**Exercise 20.1**

**Question 1: Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.**

**Solution:**

^{2}

^{2}

**Question 2: The radius of a cone is 5cm and vertical height is 12cm. Find the area of the curved surface.**

**Solution:**

^{2}= r

^{2}+ h

^{2}

^{2}= (5)

^{2}+(12)

^{2}

^{2}= 25 + 144

^{2}= 169

^{2}

**Question 3 : The radius of a cone is 7 cm and area of curved surface is 176 cm**

^{2}. Find the slant height.**Solution:**

^{2}

**Question 4: The height of a cone 21 cm. Find the area of the base if the slant height is 28 cm.**

**Solution:**

^{2}=l

^{2}-h

^{2}

^{2}= (28)

^{2}+ (21)

^{2 }

^{2}= 282 – 212

^{2}

^{2}

^{2}

^{2}.

**Question 5: Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.**

**Solution:**

^{2}= r

^{2}+ h

^{2}

^{2}= 6

^{2}+8

^{2}

^{2}= 36 + 64

^{2}= 100

^{2}

^{2}

^{2}.

**Question 6: Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.**

**Solution:**

^{2}.

**Question 7: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.**

**Solution:**

^{2}

^{2}.

**Question 8: The area of the curved surface of a cone is 60 π cm**

^{2}. If the slant height of the cone be 8 cm, find the radius of the base.**Solution:**

^{2}

**Question 9: The curved surface area of a cone is 4070 cm**

^{2}and diameter is 70 cm .What is its slant height?**(Use π= 22/7)**

**Solution:**

^{2}

**Question 10: The radius and slant height of a cone are in the ratio 4:7. If its curved surface area is 792cm**

^{2}, find its radius. (Use π =22/7)**Solution:**

^{2}

^{2}= 792

^{2}= 792

^{2}= 9

**Exercise 20.2**

**Question 1: Find the volume of the right circular cone with:**

**(i) Radius 6cm, height 7cm**

**(ii) Radius 3.5cm, height 12cm**

**(iii) Height is 21cm and slant height 28cm**

**Solution:**

^{2}h)

^{2}x 7

^{3}

^{2}h

^{2}x 12

^{3}

^{2}= l

^{2}- h

^{2}

^{2}= (28)

^{2}– (21)

^{2}

^{2}h

^{2}x 21

^{3}

**Question 2: Find the capacity in litres of a conical vessel with:**

**(i) radius 7 cm, slant height 25 cm**

**(ii) height 12 cm, slant height 13 cm.**

**Solution:**

^{2}= r

^{2}+ h

^{2}

^{2}= 7

^{2}+ h

^{2}

^{2}- 72 = h

^{2}

^{2}

^{2}

^{2}h

^{2}× 24

^{3}.

^{2}= r

^{2}+ h

^{2}

^{2}= r

^{2}+ 12

^{2}

^{2}- 12

^{2}= r

^{2 }

^{2}

^{2}

^{2}h

^{2}× 12

^{3}.

**Question 3: Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.**

**Solution:**

**Question 4: The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cubic meter, find the slant height and the radius. (Use π=3.14).**

**Solution:**

^{2}= r

^{2}+ h

^{2}

^{2}= (5x)

^{2}+ (12x)

^{2}

^{2}= 25x

^{2}+ 144x

^{2}

^{2}= 169x

^{2}

^{3}

^{2}h = 314

^{2}) × (12x) = 314

^{2}× 12x = 314 × 3 × 3.14

^{3}= 314 × 3 × 3.14

^{3}=1

**Question 5: The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use π=3.14).**

**Solution:**

**Question 6: The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. Find the ratio of their vertical heights.**

**Solution:**

_{1}) = 2x

_{2}) = 3x

_{1}) = 4y

_{2}) = 5y

^{2}h

**Question 7: A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.**

**Solution:**

^{2}h)/(1/3 πr

^{2}h)

**Exercise VSAQs.....................**

**Question 1: The height of a cone is 15 cm. If its volume is 500π cm**

^{3}, then find the radius of its base.**Solution:**

^{3}

^{2}h

^{2}x 15

^{2}x 15

^{2}

^{2}

^{2}

**Question 2: If the volume of a right circular cone of height 9 cm is 48π cm**

^{3}, find the diameter of its base.**Solution:**

^{3}

^{2}h

^{2}× 9

^{2}× 9

^{2}

^{2}= 16

**Question 3: If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.**

**Solution:**

^{2}= l

^{2}- h

^{2}

^{2}= 28

^{2}- 21

^{2}

^{2}= 784 – 441

^{2}= 343

^{2}h

^{2}× 21

^{3}.

**Question 4: The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find the diameter of its base.**

**Solution:**

^{3}

^{2}h

^{2}× 3.5

^{2}× 0.5

^{2}

^{2 }

^{2}= √900